Fock potential

In Figure 1 we show the computed and the experimental second virial for the two potentials obtained in Ref. 26, for the most widely used semi-empirical ST2 potential, and for the Hartree-Fock potential. For the third virial coefficient we refer elsewhere. ... 

The first two terms are the kinetic energy and the potential energy due to the electron-nucleus attraction. V HF(i) is the Hartree-Fock potential. It is the average repulsive potential experienced by the i th electron due to the remaining N-l electrons. Thus, the complicated two-electron repulsion operator l/r in the Hamiltonian is replaced by the simple one-electron operator VHF(i) where the electron-electron repulsion is taken into account only in an average way. Explicitly, VHF has the following two components ... 

G. C. Lie and E. Clementi, Study of the structure of molecular complexes XII Structure of liquid water obtained by Monte Carlo simulation with the Hartree-Fock potential corrected by inclusion of dispersion forces, J. Chem. Phys. 62 2195 (1975). 

The Hartree-Fock potential energy curves are necessarily unsatisfactory towards the dissociation limit, and the most reliable overall potential energy diagram for Oa is that of Gilmore,8 although it does omit certain states of interest. The curves are reproduced in Figure 1. 

More recently, Caves and Karplus71 have used diagrammatic techniques to investigate Hartree-Fock perturbation theory. They developed a double perturbation expansion in the perturbing field and the difference between the true electron repulsion potential and the Hartree-Fock potential, V. This is compared with a solution of the coupled Hartree-Fock equations. In their interesting analysis they show that the CPHF equations include all terms first order in V and some types of terms up to infinite order. They propose an alternative iteration procedure which sums an additional set of diagrams and thus should give results more accurate than the CPHF scheme. Calculations on Ha and Be confirmed these conclusions. 

Results from a HF)1 ) approach are also shown in Table 5.1. Here HF stands for Hartree-Fock, and the label indicates that the Pss(r) and PsA(r) functions are calculated in a state-dependent Hartree-Fock potential which takes into... 

TDDFRT presented in this section is also applied within the time-dependent hybrid approach. It parallels the corresponding approach in DFT and it combines TDDFRT with the time-dependent Hartree-Fock (TDHF) theory [10, 54]. Instead of a pure DFT xc potential vxca, the hybrid approach employs for the orbital (j)i(y in (7) an admixture of an approximate potential vxca with the exchange Hartree-Fock potential vxja for this orbital... 

Relations shall also be presented involving the correlation energy, HFEJn], [11], whose functional derivative is meant to be added to the ordinary Fock potential to produce, upon self-consistency, the exact ground-state energy and density. 

Hartree-Fock Potential Energy Surface Calculations Asymptotic Behaviour of Single Determinantal Wavefunctions.—In general, a single determinantal wavefunction, whether or not it is at the Hartree-Fock limit, does not provide an adequate description of a molecular system over the complete range of intemuclear separations, because of the failure of such a function to describe... 

For heavier triatomic systems, Flartree-Fock potential surfaces had earlier been calculated for FI + NO- FfNO [120] andO + NO [121]. Recently Pipano and Kaufman [122] performed an ab initio large-scale configuration-interaction calculation for the reaction 0+ + Na - NO+ + N that included all single and double excitations relative to the lowest configurations of the 2n(, 2 +, 4n, states of the intermediate NNO+ as a function of internuclear distance. These results, as an example of the melding together of the way the theoretical techniques outlined earlier complement each other and experimental observations, will be discussed in more detail in Section IV of this chapter. 

Popkie H, Kistenmacher H, Clementi E (1973) Study of the structure of molecular complexes IV. The Hartree-Fock potential for the water dimer and its application to the liquid state. J Chem Phys 59 1325-1336... 

Local Hartree-Fock potential exchange approx. ab initio... 

The type of correlated method that has enjoyed the most widespread application to H-bonded systems is many-body perturbation theory, also commonly referred to as Mpller-Plesset (MP) perturbation theory This approach considers the true Hamiltonian as a sum of its Hartree-Fock part plus an operator corresponding to electron correlation. In other words, the unperturbed Hamiltonian consists of the interaction of the electrons with the nuclei, plus their kinetic energy, to which is added the Hartree-Fock potential the interaction of each electron with the time-averaged field generated by the others. The perturbation thus becomes the difference between the correct interelectronic repulsion operator, with its instantaneous correlation between electrons, and the latter Hartree-Fock potential. In this formalism, the Hartree-Fock energy is equed to the sum of the zeroth and first-order perturbation energy corrections. 

An appropriate potential for many cases is the frozen-core Hartree—Fock potential with the addition of a core-polarisation term. 

The calculation describes the differential cross sections and 2 P electron impact coherence parameters quite well. For the 2 P differential cross section it is contrasted with a variant of the distorted-wave Born approximation, first-order many-body theory, where the distorted waves are both calculated in the initial-state Hartree—Fock potential. 

---